Mathematics vs. Physics

“Philosophy [i.e., physics] is written in this grand book--I mean the universe--which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth.” Galileo Galilei, Il Saggiatore (The Asssayer, 1616)

Galileo stood for mathematical physics; the idea that mathematics is the language of nature. Plato said this long ago, as Raphael tried to show in "The School of Athens."(Figure 1) Plato points one finger toward the ideal world of forms; according to Plato, you need mathematics to understand nature. Aristotle spreads his fingers downward toward the physical world of diverse particulars. To study physics, according to Aristotle, you don’t need mathematics. Link: Raphael, School of Athens, at the Vatican.

Galileo was surrounded by those who thought, like Aristotle, that physics should be qualitative. Galileo insisted otherwise, and turned the disciplinary hierarchy upside down: mathematicians, far from being low on the totem pole, could do physics better than the physicists. So Galileo is the supreme example of a new way of doing science: mathematical phyics.

So the modern world inherited from the Greeks two distinct approaches in the attempt to comprehend the universe:

The mathematical approach, often associated with Platonism, exemplified by Euclid, Archimedes and Ptolemy.

Non-mathematical Aristotelian physics.

Mathematicians from a century before Galileo to the generation of Newton mounted a successful attack on Aristotelian physics and replaced it with mathematical physics.